## Math Problem Statement

# The distance between two parallel lines 3 x + 4 y + c 1

# 0 3x+4y+c 1 =0 and 3 x + 4 y + c 2

0 3x+4y+c 2 =0 is 4 4, where c 2

c 1

0 c 2

c 1 0.The minimum distance between the point (2,3) and the line 3 x

# 4 y + c 1

0 3x+4y+c 1 =0 is 6 6. Find out the value of c 1 + c 2 c 1 +c 2 .

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Analytical Geometry

Distance between Parallel Lines

Distance from a Point to a Line

### Formulas

Distance between two parallel lines: |C2 - C1| / √(A^2 + B^2)

Distance from a point to a line: |Ax1 + By1 + C| / √(A^2 + B^2)

### Theorems

Distance Formula

Parallel Line Equation

### Suitable Grade Level

Grades 9-12

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